In a large enameled cast-iron casserole, heat the oil until shimmering. Add the onion, garlic, ginger and chiles and cook over moderate heat, stirring occasionally, until softened, about 5 minutes. Stir in the curry powder and turmeric and cook for 2 minutes. Add the broth and coconut milk and season with salt and pepper. Bring to a boil and simmer for 5 minutes. Add the potatoes and cook over moderate heat until barely tender, 5 minutes. Add the cauliflower and squash, cover partially and cook over moderately low heat, stirring occasionally, until the vegetables are tender, 15 minutes.